Shared Solar-powered EV Charging Stations:Feasibility and Benefits

Stephen Lee, Srinivasan Iyengar, David Irwin, Prashant ShenoyUniversity of Massachusetts, Amherst

Abstract—Electric vehicles (EV) are growing in popularity asa credible alternative to gas-powered vehicles. These vehiclesrequire their batteries to be “fueled up” for operation. While EVcharging has traditionally been grid-based, use of solar poweredchargers has emerged as an interesting opportunity. Thesechargers provide clean electricity to electric-powered cars thatare themselves pollution free resulting in positive environmentaleffects. In this paper, we design a solar-powered EV chargingstation in a parking lot of a car-share service. In such a car-share service rental pick up and drop off times are known. Weformulate a Linear Programming approach to charge EVs thatmaximize the utilization of solar energy while maintaining similarbattery levels for all cars. We evaluate the performance of ouralgorithm on a real-world and synthetically derived datasets toshow that it fairly distributes the available electric charge amongcandidate EVs across seasons with variable demand profiles.Further, we reduce the disparity in the battery charge levelsby 60% compared to best effort charging policy. Moreover, weshow that 80th percentile of EVs have at least 75% battery levelat the end of their charging session. Finally, we demonstratethe feasibility of our charging station and show that a solarinstallation proportional to the size of a parking lot adequatelyapportions available solar energy generated to the EVs serviced.

I. INTRODUCTION

Over the past few years, electric vehicles (EV) have gainedsignificant traction because of their appeal as a crediblealternative to gas-powered vehicles. Since 2008, more than4,10,000 EVs have been sold in the US alone by December2015, representing 33% of the global sales [9]. With EVsexpected to be a major source of transportation in the future,there has been meaningful discussion around their adoptionincluding those for policymakers [16]. However, EVs requirea charging station that enables them to “fuel up” its batteriessimilar to gasoline powered cars. While EVs are inherentlypollution free, the electricity used to charge their batteriesmay be drawn from traditional fossil-fuelled power plants,diminishing their appeal as an environment-friendly mode oftransport.

Recently, there is a move towards designing solar-poweredEV charging stations that provide clean electricity. With thereduction in solar costs and improvement in solar efficiency,building solar-powered EV charging station presents an excel-lent opportunity to greenify our transportation needs, makingEVs end-to-end environmentally positive. While PV systemsmay be installed on rooftops to build such charging stations,solar canopies installed on parking lots make an excellentchoice for solar-powered EV charging stations as it not onlygenerate clean electricity but also provide shade to the vehi-cle (see Figure 1).

Fig. 1. Solar canopy parking lot with EV chargers.

In our paper, we consider a solar-powered charging stationfor an EV car-share service (such as ZipCar, Autolib). Usually,in a vehicle-sharing service, gasoline powered vehicles arepopular but with rising popularity of electric cars, these serviceproviders may soon own more electric cars. In fact, somevehicle-sharing services already have Tesla models, cars thatrun solely on electricity. Typically, vehicle-sharing serviceleases vehicles to consumers and bill consumers using a pay-per-use model. When the cars are not in use, they may becharged from the power outlet until the start of the next lease.

Designing a solar-powered charging station for a car-shareservice poses interesting challenges. First, the solar canopiesmust be appropriately sized to deliver enough power to chargethe cars. While a small PV system may not deliver enough en-ergy, a large PV system may cause wastage of energy. Second,solar power is intermittent as the amount of power generatedon any given day is dependent on ambient weather conditionssuch as cloud cover and temperature. Finally, vehicles mustbe charged such that depleted batteries have a higher priorityover batteries with more charge. Obviously, a user will prefera car with more charge over a car with less charge. Thus, toimprove user satisfaction, if an electric car is 80% charged andanother car is 20% charged, charging preference must be givento the car with a lower battery level. Note that the solar powerin a given day is limited, thus if multiple cars are plugged infor charging, the best effort equal charge may be sub-optimalas it does not prioritize one car over the other.

Prior research work mostly focuses on sizing and placementof charging stations in a given location[12], [4], energy de-mand prediction of EVs [6], [11], and EV charging strategies

978-1-5090-5117-5/16/$31.00 c�2016 IEEE

Car model Battery size Range Charge rate(kWh) (mi) (kW)

Tesla S (pure electric) 70 240 10Nissan Leaf (pure electric) 30 107 6.6Chevrolet Volt (electric+gas) 18 53 3.6Mitsubishi i-MiEV (pure electric) 16 62 3.3Ford Fusion (electric+gas) 7 19 3.3

TABLE ISUMMARY OF THE ELECTRIC CARS IN THE DATASET

to reduce the impact on the power system [20]. However,they do not consider a grid-isolated solar-powered chargingstations in a car-share scenario. Here, we present an approachto apportioning solar energy to cars such that it maximizesboth solar utilization and user satisfaction. Our contributionsare as follows:

Vehicle-sharing scenario modeling. We model - (i) thebattery characteristics of cars with different charging rates andbattery sizes, (ii) energy constraints in a PV system, and (iii)the availability of vehicles in a shared system. In addition, wemodel the utility function for a shared scenario such that itmaximizes both solar utilization and user satisfaction.

Energy-allocation Framework. We develop an allocationframework that uses day-ahead solar energy prediction andground truth solar energy data to first arrive at a schedule andlater determines the actual allocation respectively.

Implementation and Evaluation. We implement our al-gorithm and simulate the solar-power charging station usingan extensive real-world EV charging trace extracted from theDataport dataset [15] to evaluate our approach. We show thatour approach prioritizes depleted batteries over batteries withmore charge so as to maximize user satisfaction level. Inaddition, we show that it is feasible to build grid-isolated solar-powered charging stations.

II. BACKGROUND

In this section, we present an overview on EVs and solar-powered charging stations. We also present our assumptionsand charging metrics used for solar energy allocation.

Overview. Electric Vehicles such as electric cars or electricscooters have an electric engine that is powered using onboardbatteries. EVs need to be plugged into power outlets forcharging when its batteries are depleted. Electric cars aregrowing in popularity and many cars such as Tesla S, ChevySpark and Nissan Leaf are available in the market. In countriessuch as China, electric two-wheelers (e.g. scooters, mopeds)are more common. The driving range of an electric car dependson the size of its battery capacity (see Table I).

Electric vehicles need a charging station — similar to gasstation — where they can be charged whenever their batteryrun low. Such an EV charging station is now being deployed atvarious locations such as highway rest stops, parking lots andpay garages. Residential owners of EVs can install a chargingstation in their garages too. Typically, EV charging stationsdraw power from the grid and use this electricity to chargeEV batteries. Thus, even though EV engines are pollution free,charging of batteries is not — since electricity used to charge

them may have been produced using traditional fossil fuels.To achieve a net end-to-end carbon-free footprint for EVs,many charging stations are beginning to adopt solar power. Aresidential owner can install solar panels on rooftops to chargethe EV batteries. Many parking lots are beginning to installsolar canopies to produce solar energy and can additionallyemploy chargers to power EVs. Figure 1 shows a deployedsolar canopy that is also equipped with a solar EV charger.

Vehicle charging objectives. Solar-powered EV chargerssuch as EV arc are completely powered by solar energy [7]. Insuch cases, the rate of charging of EV batteries is constrainedby the electricity generated by solar panels. Furthermore, ifmultiple EV cars are plugged into one charging stations andsolar electricity is constrained (i.e. sum of charging rate of allEVs is greater than current solar output), then charging stationneeds to determine how to apportion the solar energy acrosscars. Cars may be heterogeneous, and may have differentcharge levels. A simple best effort charging policy that equallydivides energy may not be the best strategy since maximizeuser satisfaction is an important goal in a car-share service.

We consider two objectives — utilization and fairness —in allocating solar energy to EVs in a car-share service.Maximizing solar utilization ensures the algorithm generatesallocation schedule such that charging stations deliver as muchsolar energy as possible and avoids waste. Fairness ensurescharging station allocates energy to maximize user satisfactioni.e. users drive off cars with sufficiently charged batteries.

Key Assumptions. We assume that users use a reservationsystem to check out and return the cars — so arrival anddeparture times of all EVs are known. In addition, cars areplugged into the charging station when parked at the car-share service station. We also assume that the EV chargingstations do not have batteries to store the excess solar energy,and excess energy is not utilized. Although storing the energymay be a better alternative, in our study, we focus on thefeasibility of running a charging station using solar poweronly. In future, we plan to study the addition of batteries ina solar-powered charging station. Note that while we evaluateour approach using electric car datasets, our approach is alsoapplicable to sharing schemes where electric bikes, Segwaysetc. are used. Although this work is primarily motivated by thecar-share service, the objectives described above are applicablein any shared environment where arrival and departure timesare known beforehand. For example, in a workplace parkinglot, the arrival and departure times can be estimated due tofixed working hours.

III. PROBLEM FORMULATION AND SYSTEM DESIGN

We first introduce the solar-charge allocation problem ina car-share service and formally derive the algorithm thatmaximizes solar energy utilization and delivers energy toelectric vehicles in a fair manner. Essentially, the problemrequires maximizing the total power supplied to EVs, andensures fair energy allocation i.e. giving priority to depletedbatteries over the ones with relatively higher charge. Formally,for a duration of T slots, given a solar energy generation

Car 1

Car 2

Car N

S(t)

!1R1(t)

!2R2(t)

!NRN(t)Solar Array

Fig. 2. Basic block diagram of a solar-powered EV charging station.

sequence hSt

i, 8t 2 [1, .., T ], N vehicles with energy demandD

i

, battery efficiencies ↵i

8i 2 [1, .., N ], and the availabilityof vehicles A

i

(t) 2 [0, 1] 8i, t, a charge allocation algorithmgenerates a fair charging sequence schedule hR

i

(t)i, whereR

i

(t) is the amount of energy delivered to vehicle i at timeslot t.

Figure 2 shows the charging station model of a solar-powered EV charging station. Specifically, there are k poweroutlets in the charging station that can be used to chargethe EV. The solar power generated, at any given time t,is distributed to the EVs and any excess power is unused.Although the amount of solar power generated is not knownin advance, the day-ahead solar power predictions can beprecomputed. In our approach, the algorithm uses the predictedsolar energy as an input to generate the charging schedule.Since the actual charging schedule may differ based on theactual solar energy generated, we later discuss how we managethe charging in practice.

A. EV Charging policy

Below, we describe our utility function that meets our dualobjective of — utilization and fairness. Later, we discuss asimple best-effort charging policy that may be used but doesnot meet the dual objectives of a car-share scenario.

1) Utility function for charging: We associate a utilityfunction U

i

i.e. dissatisfaction level the user perceives whenit receives an EV with a given battery level. Clearly, ahigher battery level translates to lower dissatisfaction leveland vice-versa. Utility function formulation helps minimizethe dissatisfaction level and ensure the vehicles are fairlycharged. Figure 4 shows a sample utility function for a user ata given battery level. This function is convex and it providesdiminishing returns at the tail-end with smaller dissatisfactionas battery level increases. Intuitively, the dissatisfaction gap ismuch higher among users who receive vehicles with a low anda high battery level. Whereas, the dissatisfaction gap is lesserwhen users receive vehicles with moderate or high batterylevel.

2) Best-effort charging: In a best-effort charging policy,the power generated per unit time can be divided equally orproportionally to the available EVs. However, such a policymay not guarantee maximum solar utilization over the day. For

EV1$

EV2$

Availability$hours$1$ 2$0$

Op6mal$Approach$

5$kWh$ 5$kWh$

Best$Effort$Charging$

2.5$kWh$2.5$kWh$

2.5$kWh$2.5$kWh$

Fig. 3. An illustrative comparison between best effort equal charging policyand an optimal approach. While best effort equal charging policy allocates7.5 kWh of solar energy, an optimal approach allocates 10 kWh.

illustration, let us consider two EVs (EV1 and EV2) availablein the charging station for 1 & 2 hours respectively, and eacharrives with an initial battery capacity of 0% and requires 5kWh of energy to reach 100% battery level (see Figure 3).For simplicity, let us assume the solar energy available perhour is 5 kWh. A best effort equal charge policy divides thecharge equally among available EVs. Thus, in the best effortpolicy, both EV1 and EV2 receives 2.5 kWh in the first hourand EV2 receives 2.5 kWh in the second hour. The policyneither maximizes utilization nor fairness, as total solar energyallocated is 7.5 kWh out of 10 kWh of available solar energy(lower utilization) and disparate battery levels of 50% and100% (less fairness). However, an optimal strategy distributes5 kWh to EV1 in the first hour and 5 kWh to EV2 in the secondhour. Since both EVs receive 5 kWh of solar energy andall the available solar energy is utilized, the optimal strategymaximizes both utilization and fairness.

Usually, best effort charging policy work in scenarios wherearrival and departure times of EVs, or solar energy generatedis unknown. However, in a car-share scenario, the availabilityof EVs is known with arrival and departure times. Thisinformation can be leveraged to derive charging schedules thatbest utilizes the available solar energy and divides the solarenergy fairly. Below, we describe our approach to allocatesolar energy fairly while maximizing utilization.

B. A LP approach to Solar-Charge Allocation

We provide a linear programming (LP) framework to solvethe offline allocation problem. The linear program takes intoaccount the solar energy generated, the energy demand foreach vehicle i, availability and battery level of each vehicle, todetermine the fair allocation while maximizing the total solarenergy delivered to the vehicles. First, we define our model.The sum total solar energy delivered to each vehicle i in timeslot t cannot exceed the total solar energy S(t) generated bythe PV panels in time slot t.

X

i

Ri

(t) S(t) 8t (1)

Fig. 4. Sample utility function to associate user dissatisfaction for a givenbattery level. While low battery level gives higher dissatisfaction, higherbattery level provides lower dissatisfaction.

where, 0 Ri

(t) Rmax

i

and Rmax

i

is the maximum chargerate of vehicle i.

We assume access to the charging station is reservationbased and the arrival and departure of each vehicle are known.In each time slot t, R

i

(t) = 0 when vehicle i is not availablefor charging. When vehicle i is available, its charging isdetermined by the availability of power outlets. Let Omax

denote the max. number of power outlets in the station. Thenumber of vehicles charging at any given time t is given by,

X

i

xi

(t) Omax 8t (2)

where, xi

(t) 2 [0, 1], denotes whether vehicle i is plugged infor charging in time slot t. Since vehicles are charged onlywhen plugged in, we must have

Ri

(t) xi

(t) ⇤Rmax

i

8i, t (3)

Next, the energy stored in the battery at vehicle i at slott + 1 must satisfy energy conservation constraint. Let Y

i

(t)denote the amount of energy stored in the battery at vehicle iat slot t. We have

Yi

(t+ 1) = Yi

(t) + ↵i

Ri

(t) 8i, t (4)

where, 0 ↵i

1 denotes the efficiency of the battery forthe ith vehicle. Energy stored in the battery at vehicle i cannotexceed its max capacity Y max

i

or underflow. We must have

0 Yi

(t) Y max

i

8i, t (5)

Let, Bi

(Tdep

) denote the battery level of the vehicle i whenit leaves at time slot T

dep

. The objective is defined as apiecewise linear function (as shown in Figure 4) of a convexfunction that aims to maximize the battery level for eachvehicle i while prioritizing depleted batteries over chargedbatteries and is defined as

minX

i

Ui

(Bi

(Tdep

)) (6)

where Ui

(.) is the utility function and defined as a piecewiselinear approximation of a convex function (see Figure 4).

Intuitively, the objective function maximizes the battery levelby minimizing the utility function U

i

(.) associated with batterylevel B

i

. In addition, the utility function is fair as lowercharged batteries have a higher dissatisfaction compared tohigher charged batteries.

C. Online Charging Algorithm

Based on availability of the EV, the above offline LP pro-duces a charging sequence schedule hR

i

(t)i, 8i, t. Dependingon factors such as weather conditions, the actual solar energygenerated may be greater or less than the predicted value.Thus, the actual solar energy S

actual

(t) generated may bemore/less from the predicted value S

predicted

(t). We adjust thecharging sequence proportionally by increasing/decreasing theR

i

(t) values. Thus, at any given time t, the charging algorithmhas the following cases:

1) If Sactual

(t) == Spredicted

(t), then do not modify theR

i

(t) values.2) If S

actual

(t) < Spredicted

(t), then divide the en-ergy proportionally by Rnew

k

(t) = Sactual

(t) ⇤R

k

(t)/P

k2A(t) Rk

(t), where A(t) = {k|(Rk

(t) >0)^ (k 2 N)} is the set of available vehicles to allocateenergy.

3) If Sactual

(t) > Spredicted

(t), then we take the followingsteps to proportionally divide the available energy:Step 1. Compute the excess energy available for alloca-tion. excess energy = S

actual

(t)�P

Ri

(t)Step 2. Divide the energy proportionally based on currentallocation to available vehicles. Rnew

k

(t) = Rk

(t) +excess energy ⇤R

k

(t)/P

k2A(t) Rk

(t),where A(t) = {k|(R

k

(t) > 0) ^ (Rk

(t) < Rmax

i

) ^((Y

k

(t) + Rk

(t)) < Y max

k

) ^ (k 2 N)} is the setof available vehicles to allocate energy such that itsconstraints are not violated.Step 3. Ensure the capacity constraints and charg-ing constraints are not violated. Ractual

k

(t) =min(Rnew

k

(t), Rmax

k

, Y max

k

� Yk

(t))Step 4. Update excess energy =

PRnew

k

(t) �PRactual

k

(t)Step 5. Repeat step 2 until excess energy is zero orno vehicles left to allocate the excess energy to. i.e.excess energy == 0 or |A(t)| == 0In other words, at each iteration, the algorithm dis-tributes the excess energy to available vehicles andrepeats until no energy is left to distribute or all thevehicle constraints are met.

IV. EVALUATION METHODOLOGY

We evaluate our solar-charge allocation algorithm usingboth synthetically generated data and the Dataport dataset1 —a real-world trace comprising, in part, power consumption ofEVs and power generation of solar panels located in Austin,Texas. The dataset includes detailed information such as theamount of energy used to charge the battery, the time of the

1http://dataport.pecanstreet.org/

Number of Cars 97Car Sessions used 9083 out of 12123

Median Charging Session 65 minutesMedian Car’s Energy Demand 3.31 kWhMedian Daily Energy Demand 104.8 kWh

Solar panel Size 18 kWMedian Daily Solar Energy 74.5 kWh

TABLE IISUMMARY OF CARS AND SOLAR INSTALLATION IN EV DATASET

day and the duration a car is connected to a power outlet.It also contains solar power generation traces from multipleresidential buildings. Further, our dataset is at a minute levelgranularity collected for a three-year period.

To simulate the charging operations of a car-share servicewith a solar-power charging station, we construct an EVdataset combining the EV and solar data described above.First, we assume that the solar-powered EV charging stationhas 5 power outlets. Since the charging station can service amaximum of five vehicles at any given time slot, we constructour EV charging dataset by making a simplifying assumptionthat the vehicles are selected from the dataset on a first-come-first-serve (FCFS) basis until all power outlets are occupiedfor any given time slot. We refer each contiguous interval ofcharging by a vehicle in the dataset as a charging session.Since the vehicles can be charged only when solar energy isavailable, we consider only those charging sessions that chargeafter sunrise and before sunset (see Table II). Collectively, thedataset contains 9083 charging sessions. Further, we assumethat the amount of charge drawn during a given chargingsession is the amount needed to fully charge its battery.

PV system sizing: We first determine the size of the solarpanel needed to cover a single car in a parking lot. Thedimension of a single parking lot for a car in the US is around9 ft. X 18 ft — a total area of 162 sq.ft. A typical solar panelof size 17.57 sq. ft. produces 345 watts2. Thus, the amountof solar power generated from a single parking lot is around3.2 kW. and a parking lot with 5 vehicles can generate around18 kW. Unless stated otherwise, we use a 18 kW PV systemfrom the dataset for our evaluation. We select a residentialrooftop installation from the Dataport dataset that has a solargeneration capacity of 18 kW. We use this as the ground truthfor actual solar power generated. Our algorithm requires thepredicted solar energy values to initially schedule the chargingand later uses the actual solar energy trace for allocating chargeto the EVs. We employ the methodology described in [10] thatuses the solar panel’s characteristics and day-ahead weatherforecasts to compute the predicted solar power. We train themodel using the dataset available for the previous year (2014)and predict the solar power generated for the year (2015).For our evaluation, we assume there is no loss in deliveringsolar energy to the cars i.e ↵ = 1. In addition, we evaluateat 5 minutes granularity as we wanted to ensure 5 minutes ofuninterrupted charging of batteries.

Utility function: In our LP formulation, to improve theruntime, we assume a piecewise linear approximation of the

2SunPower X21 panel

Fig. 5. Mean and standard deviation of the battery levels. Our approach showa 60% lower std. deviation compared to best effort indicating fairer allocation.

convex function as shown in Figure 4. We define the piecewiselinear approximation as follows:

Ui

(x) =

8>>><

>>>:

100� 2.4x, 0 x < 25

65� 1.0x, 25 x < 50

35� 0.4x, 50 x < 75

17� 0.16x, otherwise.

The utility function Ui

(.) is chosen such that for a givenbattery level range (e.g. 0% to 25%), the LP may choose todistribute energy to any EV having battery level within therange. However, between the different battery level ranges,the LP priorities lower battery such that U

i

(Bi

([0, 25))) >Ui

(Bi

([25, 50))) > Ui

(Bi

[50, 75))) > Ui

(Bi

[75, 100))). Inother words, cars with battery level between [0% to 25%] hasa higher dissatisfaction than cars with battery level greaterthan 25%. Note while we select a linear approximation for ourevaluation, other linear approximation of a decreasing convexfunction may be used.

V. EXPERIMENTAL RESULTS

A. Utilization and Fairness analysis

We compare the fairness and utilization of our approachto the best effort equal charging policy. As discussed earlier,the best effort charging policy distributes the available solarenergy equally among the cars available. As different EVshave varying charging rate and battery capacity, the best effortcharging policy may not maintain similar battery levels. Inthe trivial case, where solar energy available is more than theoverall EV demand, the performance of our approach and thebest effort charging policy would be similar, as all the energydemand can be easily met. However, for a more pertinentevaluation, we consider the case where demand is more thanthe overall solar energy available. In particular, we consider5 cars from the EV dataset having a median charging rate of3.3 kW. We assume the cars are available for the entire daywith aggregate energy demand from EVs to be 3 times thatof the solar energy available. In addition, we uniformly assignan initial battery level between 0% to 60% to the 5 EVs for

the solar trace of August 2nd 2015 and repeat this experiment25 times. We compute the mean and standard deviation of thebattery levels for each run.

Figure 5 shows the comparison of our approach with thebest effort equal charging policy. Note that distribution ofthe mean battery level for both the methods across differentruns is similar. In particular, the average value of the meanbattery level for both the approaches is ⇡52% suggestingboth methods deliver an equal amount of solar energy to thevehicles. However, the distribution of the standard deviationof the battery levels for our approach is tighter with a loweraverage value compared to those of the best effort chargingpolicy. Clearly, a fair allocation will ensure cars depart atsimilar battery levels and will have lower standard deviation.In particular, we observe that using our approach the averagevalue of the standard deviation is ⇡8%, whereas using the besteffort charging policy the standard deviation is ⇡20%. Thus,our approach is more fair compared to the best effort chargingpolicy as the average value of the standard deviation of ourapproach is lower by ⇡60%.

B. Battery level analysis

We empirically analyze the utilization of solar energy usingthe EV dataset for the entire year. Charging sessions in theEV dataset is used to simulate the arrival and departure timesalong with energy demands for EVs serviced in a car-sharecharging station. Solar energy is allocated using our approach,and we compute the battery level of each car at the end of thecharging session. Figure 6 shows the frequency distribution ofthe initial and final battery level of cars charged over the entireyear. As expected, we observe an increase in the number ofcars leaving the charging station with a higher battery level.We observe that the 80th percentile of the cars have at least75.08% battery level at the time of departure. Among thesecars, some had an initial charge as low as 1.79%.

C. Impact of solar power intermittency in charge allocation

As discussed earlier, the offline LP algorithm uses theday-ahead solar energy predictions to generate the chargeallocation schedule, and the online algorithm uses the groundtruth solar trace to allocate the charge. Due to solar energyprediction errors, the charge allocation schedule generated bythe offline algorithm differs from the online algorithm. Here,we analyze the mismatch in the charge allocation schedulegenerated by the offline and the online algorithm.

1) Synthetic dataset with poisson arrivals: We use thecar’s charging session and other attributes from the real-worlddataset to construct the synthetic dataset. However, we ignoreits original arrival time and assume it to be generated from aPoisson process with a fixed rate. First, we run our offline LPapproach and then the online algorithm to compute the overallenergy delivered in a given day. We run our simulation for aweek in each season. Figure 7 shows the difference in energyestimated by the offline LP approach and the energy deliveredby the online algorithm with an arrival rate of 2 cars per hour(� = 2). As shown in the graph, our offline algorithm estimate

Fig. 7. Difference in overall energy estimated by the offline and the energydelivered by the online approach to the cars with poisson arrival rate of 2cars per hour

Fig. 8. Difference in overall energy estimated by the offline and the energydelivered by the online approach to the cars using real-world dataset for theentire year

is between -4% to 4% on most days. Since the solar predictionworks considerably well during summer days, we notice thatthe mismatch in summer is smaller compared to other seasons.

2) Real-world dataset: Unlike the previous evaluation, weuse the arrival times in addition to other car attributes availablein the dataset. Figure 8 shows the difference in energy esti-mated by the offline LP approach and the energy delivered bythe online algorithm for the entire year. As the figure shows,the mismatch is less than 5% for all but 2 days, and less than1% for 287 days. Moreover, the mismatch is negative for somedays i.e. more energy is given to the cars than offline algorithmhad estimated. Since the solar model may predict a lower solarenergy value for the day-ahead, the actual energy allocated tothe cars by the online algorithm can be higher than the offlineapproach.

D. Feasibility analysis of solar-powered charging station

Evaluating the feasibility of our solar-powered chargingstation requires us - (i) to validate the sizing of the PVsystem installed, (ii) demonstrate the utilization of solar energyavailable, and (iii) exhibit fulfillment of EVs charge demand.In this section, we assess the performance of our approach onthese parameters. Similar to the earlier evaluation, we test ouralgorithm on both synthetic and real-world traces.

1) Synthetic dataset: To construct the synthetic dataset weconsider the following scenario. We assume the car-share

(a) Initial battery level of cars at arrival (b) Final battery level of cars at departureFig. 6. Battery levels of cars before/after charging at the charging station for the entire year.

service operates 5 Chevrolet Volt cars. With a maximumcharge rate of 3.6 kW and battery size of 18 kWh, starting withan empty battery these cars take typically 5 hours to chargeto full capacity (see Table I). For our evaluation, we assumethe cars are available for the 5-hour duration to charge theirbatteries. In addition, we uniformly choose the arrival time forthe five EVs between 9 a.m. to noon to ensure that the solarenergy is available when they are plugged in. We select thesolar trace of August 2nd 2015 and vary the solar installationsize to compute the overall EV demand fulfilled and the solarenergy utilized by the charging station. To reduce specificityto a random sample, we repeat the experiment 25 times andtake its average value.

Figure 9 shows the average demand fulfilled and solarenergy utilized over several runs when solar installation sizeis varied between 2 to 36 kW. As expected, smaller sizedPV system has a higher solar utilization whereas the demandfulfilled is lower, as most of the solar energy generated isdelivered to the cars. As we increase the solar installation size,we notice diminishing returns in terms of demand fulfilled.This is due to lower power generation by the solar installationduring morning and evening period. Even with increasedsolar capacity, the gap between the energy demand fromEVs and the available solar energy does not decrease rapidly.The shaded region in the figure highlights a reasonable PVinstallation size (13.5-22.5 kW) that maximizes both demandfulfillment and solar utilization. Further, we observe that withPV installation size of 18 kW, the solar utilization is as highas 67% and energy demand fulfilled is around 68%.

2) Real-world dataset: We now evaluate the feasibilityof solar-powered charging station for the real-world dataset.Similar to the previous evaluation, we vary the solar in-stallation size to compute the overall EV demand fulfilledand the solar energy utilized for the entire year. Similar tothe synthetic dataset evaluation, we observe that smaller PVinstallations tend to have higher solar utilization but lowerdemand fulfillment. It is interesting to note that the knee pointis around 18 kW, the energy generated by the size of a parkinglot that we had estimated earlier. In addition, the highlightedregion around the knee point is the typical range of a PVsystem size that can be installed in a parking lot.

Fig. 9. Variable solar installation size with average solar utilization anddemand fulfillment using the synthetically constructed dataset.

Fig. 10. Energy demand fulfilled and solar utilized using the real-worlddataset for the entire year. The highlighted region shows the typical PVsystems size that can be installed in a parking lot for 5 cars.

VI. RELATED WORK

The increasing popularity of EVs raises a myriad of chal-lenges. In this section, we provide a brief overview of re-search focussed on resolving such challenges. The impact ofintegrating EVs into the grid has been well studied. Li et. al.introduces a conceptual framework for integrating EVs into thegrid and discusses its impacts and benefits [13]. Taylor et. al.presents an analysis by accounting the impact of for spatialand temporal diversities in EVs on the distribution feedersof varying characteristics [18], and Foley et.al. discusses theimpact of EVs charging on electricity markets [8].

An important aspect in evaluating the EVs demand is right-

sizing and placement of charging stations. Chen et. al. presentsa city-wide study to find constrained number of optimal charg-ing station locations by minimizing the cost of accessing themby EV users [4]. Liu et. al. introduces a two-step approachwhere initially candidate sites are initially selected based onenvironmental factors and the service radius of EV chargingstations [12]. Also, a mathematical model is presented thatcalculates an optimal sizing of EV charging stations. Swedaet. al. discusses an agent-based decision support system foridentifying patterns in residential EV ownership and drivingactivities for setting up charging station infrastructure [17].However, our work is complementary as we consider chargeallocation in a shared charging station and not setting up ofcharging station infrastructure in different locations. Moreover,one-time planning of locating the stations does not completelyguarantee the operational challenges of charging individualEVs to maintain customer satisfaction. Thus, a reasonablecharging strategy is required for optimizing operational needs.

Prior works have also examined various charging strategiesthat satisfy different objectives. These objectives include - (i)leveraging ToU pricing to optimize costs [2] [20], (ii) improv-ing voltage profile [5], (iii) flatten grid electricity profile [21],and (iv) flatten residential electricity profile [14]. In addition,previous works have used EV batteries as a source to powerresidential homes to get a grid friendly load profile [1]. Thiswork addresses the problem of a grid-isolated solar-powercharging station in a car-share service, which differs fromprevious work discussed above. Further, in a car-share service,the flexibility in scheduling cars may not be present to leveragesome of the strategies presented above.

Co-benefits of renewable integration with EVs have beenstudied in the literature. However, these studies focus eitheron reducing intermittency of renewable sources of energy [3][19] or on large-scale aggregated energy demand placed byEVs and the potential renewable energy available (wind andsolar) [6], [11]. However, these work do not present actionablecharging strategies that we address in this paper.

VII. CONCLUSION

In this paper, we explored the benefits of integrating re-newable solar energy with EV charging infrastructure placedat car-sharing service’s parking lot. We formulated a LinearProgramming approach that maximized both solar energy uti-lization and customer satisfaction. Comprehensive evaluationof our algorithm was performed using real-world EV chargingtraces. We show that our algorithm fairly distributes the chargeamong candidate EVs and improves the disparity in batterycharge levels by 60% compared to the best effort chargingpolicy. Our results indicate that the 80th percentile of the EVshave at least 75% charge at the end of their charging session.Further, we assessed the performance of our approach acrossdifferent seasons with variable demand profile. Finally, wedemonstrated the feasibility of a grid-isolated solar-poweredcharging station and show that a PV system proportional tothe size of a parking lot adequately apportions available solarenergy generated to the EVs serviced.

Acknowledgements. This research is supported by NSFgrants IIP-1534080, CNS-1405826, CNS-1253063, CNS-1505422, and the Massachusetts Department of Energy Re-sources

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